"They're celebrating this self-inflicted tragedy instead of celebrating the life of my father, who won three Emmys.... Cory Monteith never won an Emmy," Adam Klugman said.
Despite the criticism, Monteith's late co-star remembered the young "Glee" star during Sunday night's show.
"It is remarkable, and perhaps a little curious, how quickly TV shows become like family in some ways," Lynch began.
"This summer on our show Glee, we suffered a painful death in our family. Cory Monteith played Finn Hudson, a star quarterback-turned wide-eyed heartfelt glee singer. And from the first time you saw Cory, he had a star quality and genuine sweetness that made it impossible not to fall in love with him. And millions did fall in love with Cory."
"I'm here to say that all that warmth and that charm, that open-hearted quality that we loved in Cory was no act. Cory was a beautiful soul," Lynch continued.
As the award show's executive producer, Ken Ehrlich, promised over the weekend, Lynch's tribute also mentioned the substance abuse that led to Monteith's tragic passing.
He was not perfect, which many of us here tonight can relate to. His death is a tragic reminder of the rapacious, senseless destruction that is brought on by addiction. Tonight, we remember Cory for all he was, and mourn the loss for all he could have been. To a generation that loved Cory so, please know that this gifted and wonderful young man was worthy of your love. And if you were lucky enough to know Cory as we did and witnessed first-hand Cory's goofy, breezy sense of humor, his natural instinct for inclusiveness and his unbridled sense of generosity, day in and day out, I promise, you would have loved him even more."